Extending the Harper Identity to Iterated Belief Change

In Proceedings of the International Joint Conference on Artificial Intelligence (IJCAI) (2016)
Download Edit this record How to cite View on PhilPapers
Abstract
The field of iterated belief change has focused mainly on revision, with the other main operator of AGM belief change theory, i.e. contraction, receiving relatively little attention. In this paper we extend the Harper Identity from single-step change to define iterated contraction in terms of iterated revision. Specifically, just as the Harper Identity provides a recipe for defining the belief set resulting from contracting A in terms of (i) the initial belief set and (ii) the belief set resulting from revision by ¬A, we look at ways to define the plausibility ordering over worlds resulting from contracting A in terms of (iii) the initial plausibility ordering, and (iv) the plausibility ordering resulting from revision by ¬A. After noting that the most straightforward such extension leads to a trivialisation of the space of permissible orderings, we provide a family of operators for combining plausibility orderings that avoid such a result. These operators are characterised in our domain of interest by a pair of intuitively compelling properties, which turn out to enable the derivation of a number of iterated contraction postulates from postulates for iterated revision. We finish by observing that a salient member of this family allows for the derivation of counterparts for contraction of some well known iterated revision operators, as well as for defining new iterated contraction operators.
Categories
(categorize this paper)
PhilPapers/Archive ID
CHAETH-5
Revision history
Archival date: 2017-09-27
View upload history
References found in this work BETA

No references found.

Add more references

Citations of this work BETA

No citations found.

Add more citations

Added to PP index
2017-09-27

Total views
19 ( #37,841 of 39,984 )

Recent downloads (6 months)
8 ( #34,650 of 39,984 )

How can I increase my downloads?

Downloads since first upload
This graph includes both downloads from PhilArchive and clicks to external links.